Problem: Simplify the following expression: $ x = \dfrac{-10y - 3}{y - 1} + \dfrac{2}{7} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-10y - 3}{y - 1} \times \dfrac{7}{7} = \dfrac{-70y - 21}{7y - 7} $ Multiply the second expression by $\dfrac{y - 1}{y - 1}$ $ \dfrac{2}{7} \times \dfrac{y - 1}{y - 1} = \dfrac{2y - 2}{7y - 7} $ Therefore $ x = \dfrac{-70y - 21}{7y - 7} + \dfrac{2y - 2}{7y - 7} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-70y - 21 + 2y - 2}{7y - 7} $ $x = \dfrac{-68y - 23}{7y - 7}$